Set Theory and Logic

1801 Submissions

[4] viXra:1801.0380 [pdf] submitted on 2018-01-27 22:55:45

Refutation of the Direct Correspondence of Quantum Gates to Reversible Classical Gates © Copyright 2018 by Colin James III All Rights Reserved.

Authors: Colin James III
Comments: 1 Page. © Copyright 2018 by Colin James III All rights reserved.

These quantum gates do not directly correspond to reversible classical gates: CNOT (XOR, Feynman); Toffoli (AND); X (NOT); and n-qubit Toffoli (AND). Hence quantum gates cannot map to bivalent logic. This paper demonstrates the shortest refutation.
Category: Set Theory and Logic

[3] viXra:1801.0253 [pdf] submitted on 2018-01-19 16:14:43

Refutation of Neutrosophic Soft Lattice Theory © Copyright 2018 by Colin James III All Rights Reserved.

Authors: Colin James III
Comments: 2 Pages. Papers by and relating to Florentin Smaradnache span many areas at viXra, but the appropriate field is Set Theory and Logic. Many of them are translated as crude ruse to garner publicity. The study neutrosohic logic is mostly specious.

We evaluate the neutrosophic logic based on its most atomic level of soft latices, as published by Springer-Verlag in 2016. We refute the theorem "Every neutrosophic soft lattice is a one-sided distributive neutrosophic soft lattice." This brief evaluation implies that the field of soft set theory as originally introduced by D. Molodtsov is suspicious and specifically that the field of neutrosophic logic, as evidenced in its basis of soft set theory, is unworkable. This conclusion is multitudinal because of the plethora of duplicated papers as translations in multiple fields at vixra.org regarding the neutrosophic logic system of Florentin Smarandache.
Category: Set Theory and Logic

[2] viXra:1801.0188 [pdf] submitted on 2018-01-16 09:29:47

Refutation of the Halting Problem: not a Problem

Authors: Colin James III
Comments: 2 Pages. © Copyright 2018 by Colin James III All rights reserved.

Alan Turing's difficulty was in expressing the halting problem in the format of a two-valued logic which was not as expressive as in a four-valued logic to show nuances of what exactly the equation stated. In comparison to Gödel's incompleteness theorems, Turing's halting problem has no superficial similarities other than being refuted as not a problem. Hence in contrast, both expressions are disparate and ultimately unrelated as to content meaning. Therefore: The assumption that there is a consistent and complete axiomatization of all true first-order logic statements about natural numbers must be tautologous.
Category: Set Theory and Logic

[1] viXra:1801.0122 [pdf] submitted on 2018-01-11 01:52:00

The Incalculable Continuum

Authors: Miguel A. Sanchez-Rey
Comments: 1 Page.

A continuum in sight.
Category: Set Theory and Logic